Michael Wheeler (CU) Hyperprincipal Realizations of Ultrafilters, Part 1
Tue, Oct. 1 4pm (MATH 350)
Juan Moreno (CU) Complex Oriented Cohomology Theories
We present a functorial construction which, starting from a congruence of finite index in an algebra, yields a new algebra built from the congruence blocks. As an application we show that supernilpotence of congruences is decidable.
The categorification of the Hopf algebra of symmetric functions by the representation theory of the symmetric group is a fundamental result in combinatorial representation theory. While some of our favorite graded Hopf algebras have some representation theoretic interpretations via finite dimensional algebras, very few have come from a tower of groups (as in the symmetric group case). This talk gives a tour of recent successes in realizing graded Hopf algebras via towers of groups and their representation theory. We begin with the established case of symmetric functions in noncommuting variables and then quickly moving on to newer cases (including the Malvenuto—Reutenauer algebra). This work is joint with F. Aliniaeifard.